CHAPEL HILL, N.C.—A 46-year-old man was charged with three counts of murder in the shooting of three Muslims—a husband, wife and her sister. The alleged killings were quickly condemned as hate crimes by the victim’s family and some Muslim groups, but a prosecutor in the case said it was too early to determine whether the violence was motivated by religion.

Craig Stephen Hicks was charged with the killing Tuesday of Deah Shaddy Barakat, 23, and his wife Yusor Mohammad, 21, of Chapel Hill, and Razan Mohammad Abu-Salha, 19, of Raleigh. Each was found shot in the head and pronounced dead at the scene, a quiet condominium complex near the University of North Carolina campus. The young couple lived in the complex, and Mr. Hicks also lived there for about six years, according to police, public records and a family member.

Mr. Hicks turned himself in late Tuesday at a neighboring sheriff’s office in Chatham County, according to Chapel Hill police. Police said he was cooperating with investigators.Craig Stephen Hicks was arrested on three counts of murder early Wednesday. ENLARGECraig Stephen Hicks was arrested on three counts of murder early Wednesday. Photo: Chuck Liddy/The News & Observer/Reuters

On Wednesday, he appeared briefly in a courtroom on the first floor of the Durham County Detention Facility. Mr. Hicks wore an orange jumpsuit and kept his back to the small courtroom crowd. He is being held without bond and was told a public defender would be appointed to represent him.

Chapel Hill police said Wednesday the crime was motivated by an ongoing neighbor dispute over parking. But relatives and some Muslim groups said they believed the shootings were motivated by religion.

Mohammad Abu-Salha, father of the two sisters, said his older daughter Yusor had told him that they had a neighbor who was harassing them because of their faith. Both of his daughters were faithful Muslims who wore traditional headscarves, Dr. Abu-Salha said.

“Our daughter on more than two occasions said this man was hateful. He was picking fights, knocking on their door,” said Dr. Abu-Salha, who practices psychiatry in Clayton, N.C. “She said, ‘Daddy, this man hates us for who we are.’ ”

Mr. Hicks’s lawyer couldn’t be immediately reached for comment.

Durham County District Attorney Roger Echols said in an interview after the hearing that it was “premature” to say whether additional hate-crime enhancements might be added to the murder charges. He said it was too soon to say what role religion played, if any. “We’ll see where the investigation takes us after reviewing the findings,” Mr. Echols said. “I haven’t ruled out anything or ruled in anything.”

On what appeared to be Mr. Hicks’s personal Facebook page, numerous statements were posted attacking religion in general, and he identified himself as an atheist.

One post says, “Given the enormous harm that your religion has done in this world. I’d say I have not only a right, but a duty, to insult it.” The post doesn’t mention any specific religion.

One photograph simply is a handgun in its holster. The added comment reads: “Yes, that is 1 pound 5.1 ounces for my loaded 38 revolver, its holster, and five extra rounds in a speedloader.”

Chief Chris Blue, of the Chapel Hill Police Department, said, “We understand the concerns about the possibility that this was hate motivated. We will exhaust every lead to determine if that is the case.”

Mr. Barakat was a second-year student in the UNC School of Dentistry, and his wife had planned to begin her dental studies in the fall, according to UNC. Her sister was a sophomore at N.C. State University, majoring in environmental design in architecture, according to UNC.

Dr. Abu-Salha said his younger daughter Razan was living at home and had gone over to her sister’s to have fun. “She went to her death,” he said.

Dr. Abu-Salha and his wife moved to the U.S. in 1994 from Jordan, and both of his daughters were born in the U.S., he said. His son-in-law was the American-born son of Syrian immigrants, he said.

“We had more love and acceptance in America than hate,” Dr. Abu-Salha said. “We lived the American dream, and we were happy.”

Social media erupted Wednesday with expressions of sympathy for the slain young people and questions about whether the homicides were hate crimes.

The Council on American-Islamic Relations, a Muslim civil-liberties group based in Washington, D.C., called on authorities to move quickly to address public concerns.

“We urge state and federal law-enforcement authorities to quickly address speculation of a possible bias motive in this case,” executive director Nihad Awad said in a statement.

The crime-scene tape had already been removed on Wednesday afternoon in the small parking lot outside the brick, brown-shingle-roofed condominium building where the shooter and victims lived. Three small pots of pink flowers had been placed on the corner beside the unit where the couple lived.